# In a Simultaneous Throw of a Pair of Dice, Find the Probability of Getting: an Even Number on One and a Multiple of 3 on the Other - Mathematics

In a simultaneous throw of a  pair of dice, find the probability of getting:

an even number on one and a multiple of 3 on the other

#### Solution

$\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }:$
$S = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \cdots\left( 6, 5 \right), \left( 6, 6 \right) \right\}$
$\text{ Hence, the total number of outcomes is 36 } .$

$\text{ Let A be the event of getting pairs with an even number on one die and a multiple of 3 on the other }.$
$\text{ The pairs with an even number on one die and a multiple of 3 on the other are } \left( 2, 3 \right), \left( 2, 6 \right), \left( 4, 3 \right), \left( 4, 6 \right), \left( 6, 3 \right) \text{ and } \left( 6, 6 \right) .$
$\text{ Hence, the number of favourable outcomes is 6 }.$
$\therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 26 Data Handling-IV (Probability)
Exercise 26.1 | Q 3.07 | Page 15